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Question
Simplify:
\[\frac{x^2 - 5x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{x^2 - 64}{\left( x - 8 \right)^2}\]
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Solution
It is known that,
a2 − b2 = (a + b) (a − b)
a3 − b3 = (a − b)(a2 + ab + b2)
\[\ \frac{x^2 - 5x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{x^2 - 64}{\left( x - 8 \right)^2}\]
\[ = \frac{x^2 - 8x + 3x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{\left( x \right)^2 - \left( 8 \right)^2}{\left( x - 8 \right)^2}\]
\[ = \frac{x\left( x - 8 \right) + 3\left( x - 8 \right)}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{\left( x + 8 \right)\left( x - 8 \right)}{\left( x - 8 \right)\left( x - 8 \right)}\]
\[ = \frac{\left( x + 3 \right)\left( x - 8 \right)}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{\left( x + 8 \right)\left( x - 8 \right)}{\left( x - 8 \right)\left( x - 8 \right)}\]
= 1
RELATED QUESTIONS
Simplify:
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
Simplify:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
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`(1 - 2x + x^2)/(1 - x^3) xx (1 + x + x^2)/(1 + x)`
Factorise:
27m3 − 216n3
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`16a^3 - 128/b^3`
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Simplify: (a - b)3 - (a3 - b3)
Factorise the following:
27x3 – 8y3
Factorise the following:
a6 – 64
